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RenderCache

Solid Angle qns

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hi! I was reading on the solid angle on mathworld, but I could not understand some portions. When rewriting the first equation to cartesian form, it states that: n.da = cos(phi) dx dy how could we prove it? and simply understand where the x,y components come from? SolidAngle thx! RC

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Quote:
Original post by RenderCache

n.da = cos(phi) dx dy

how could we prove it?


It's just the relationship between the area on the face of the cube and the solid angle. Consider a square cube face centred on a pole of the sphere. The area 'n.da' is at a point sperated by phi from the pole. If you project that area onto the area dx . dy on the square then the ratio of the area on the square to that on the sphere is cos(phi), from basic trigonometry.

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